Let $G=(V,E)$ be a DAG and let $v_0\in V$. Alice and Bob are playing a game in which every player has his own turn and Bob is starting. In every turn $i$, the player is picking an edge $e=(v_i,x)$, then $x$ become $v_{i+1}$ and then it becomes the other player's turn. The player which doesn't have an edge to choose (the vertex $v_i$ has no out edges) is losing.
Propose an algorithm which determines if Bob has a winning strategy.